# User talk:Martin Hogbin/Speed of light fixed

This is the page for discussion of the 'Speed of light fixed' page.

## Comments from Brews_ohare

Martin your first two sections of this article strike me as clear and correct. The third section contains the line "The SI system is therefore following the general trend to use fundamental constants to define units rather than physical artifacts." that I find needs some amplification, but that can wait.

The fourth section, Part 1 "What if the speed of light changes?" also is fine with me.

The fourth section, Part 2 "What if it is discovered that the speed of light varies with frequency (or some other property)?" causes me one difficulty. I'd like to discuss that difficulty:

There is good evidence that the speed of light does not vary with frequency within the current limits of uncertainty of realization of the meter …

I'd agree with an alternative wording: There is good evidence that the speed of light in various real media approximating ideal vacuum does not vary with frequency within the current limits of uncertainty.
The following sentences include: "if it was found that the speed of light varied very slightly with frequency, the standard would undoubtedly be updated to allow for this." I gather the rest of this section is consistent with a definition of the metre something along the lines of: "the metre is the distance traveled by light at frequency of ω in 1/299,792,458 s". Some other possibilities are mentioned, but I believe I'd agree with them too.

So there is very little to argue about here, IMO. What do you think? Brews ohare (talk) 18:05, 14 September 2009 (UTC)

There is no need to specify that the experiments supporting the assertion that the speed of light does not vary with frequency refer to real media. We have discussed this many times before. Yes, the actual experiment (observation) was done in the real medium of outer space and it is therefore good evidence (not proof) that the speed in outer space does not vary with frequency. However, the fact that the speed of light is not observed to vary with frequency in outer space is good evidence (not proof) that it does not vary in free space. Martin Hogbin (talk) 18:25, 14 September 2009 (UTC)
Martin: We don't really need "proof" that the speed of light does not vary with frequency in free space, because according to the NIST/BIPM definition of free space it is governed by the defined electric constant and the defined magnetic constant, which have no frequency dependence at all. Free space is a hypothetical medium, with defined EM parameters, and not subject to measurement. Unless you are suggesting that Maxwell's equations as we know them might change in such a way that media with dispersionless constants would begin to exhibit dispersion anyway, and no longer would c02 = 1/(ε0μ0), even hypothetically. That kind of conjecture is surely not mainstream.Brews ohare (talk) 18:54, 14 September 2009 (UTC)
I think you have answered your own question. If the speed of light were found to vary with frequency then Maxwell's equations would have to be rewritten. People do experiments to verify current theories. That is to say they generally expect a result that is consistent with the current theory, in this case no variation of speed with frequency. However, every now and again the result does not agree with the current theory, as in the MM experiment for example, then the theory needs to be rewritten. Even then, he old theory may still be perfectly adequate for most purpose, as is the case with Newtonian physics.Martin Hogbin (talk) 22:07, 14 September 2009 (UTC)
Martin: I posed no question. I stated that given Maxwell's equations and the electric constant and the magnetic constant there is no way dispersion can occur in free space. Because free space is a hypothetical model with these parameters, experiment to "verify" that a hypothetical medium has its postulated hypothetical properties is impossible in principle. All that experiment can do is to check whether a particular real medium, like outer space, is well-modeled by the ideal model of free space. That is an entirely different matter, as you know. Basing a "mainstream" discussion upon an as yet unverified conjecture that maybe Maxwell's equations will have to be altered somewhere in the future is, well, not mainstream. Brews ohare (talk) 22:26, 14 September 2009 (UTC)
That is why we do experiments. To confirm that the mainstream theory is correct. When they give the 'wrong' results we have to change the theory. That is exactly what happened with the MMX. The mainstream theory was a simple fixed aether so M and M did an experiment to confirm that theory. Rather unexpectedly, it did not do that and a new theory was required. Martin Hogbin (talk) 23:04, 14 September 2009 (UTC)
You said 'Unless you are suggesting that Maxwell's equations as we know them might change in such a way that media with dispersionless constants would begin to exhibit dispersion anyway'. That is exactly what might have to happen. Martin Hogbin (talk) 22:40, 14 September 2009 (UTC)
Sure, and it might not happen. A case could be made that no change in Maxwell's equations will ever have to be made to account for observed dispersion, only changes in the EM parameters ε, μ of the medium being measured. That is what is happening with Quantum vacuum and QCD vacuum.
You can change either. The point is that if a variation of speed with frequency were observed then some part of the theory would have to change. Martin Hogbin (talk) 23:11, 14 September 2009 (UTC)
Martin: Within this discussion changing Maxwell's equations and changing ε, μ are not equivalent types of change. The point is not that something has to change. The point is that with the present Maxwell relations dispersion in free space is logically impossible. No experiment can be done to check what is true by definition. Brews ohare (talk) 23:56, 14 September 2009 (UTC)
What exactly are you claiming is true by definition? Can you supply a link to the definition please. Martin Hogbin (talk) 09:59, 15 September 2009 (UTC)

[Brews, can we keep this in sequence please]Isn't speculation over far-distant possible happenings a little off-topic here? Brews ohare (talk) 22:56, 14 September 2009 (UTC)

There is no speculation. An experiment was done to confirm current mainstream theory and, in this case, it does exactly that. That is why I said, 'There is good evidence that the speed of light does not vary with frequency...'. Experiment confirmed what was believed to be the case. Martin Hogbin (talk) 23:22, 14 September 2009 (UTC)
##### Speed

I notice some careful wording that I understand as somehow intended to differentiate your views from mine:

Note that there is no suggestion that the light referred to here is some formal or conventional version of light, it is just, ordinary, real, physical if you like, light.

I have no problem with this.

That is to say real light actually travels (usual conditions) at exactly 299 792 458 metres per second.

I find this statement to be true, but elliptic. It doesn't elaborate how the switch to "time-of-transit" from "counting fringes" was arrived at, and so avoids the issue of how "exactly" got in here.

I wonder if at this point you have any objections to User:Brews ohare/Speed of light (Example)? Brews ohare (talk) 18:20, 14 September 2009 (UTC)

Short answer, 'Yes'. I will reply more fully later.
I really cannot see your point Brews. If a meter was defined as the distance that real physical light travels in 1/7 second then the speed of real physical light would have to be exactly 7 metres per second. How could it be anything else? Martin Hogbin (talk) 21:57, 14 September 2009 (UTC)
I assume you are talking about User:Brews ohare/Speed of light (Example). The objective, as stated at the outset, is to differentiate between c as measured using, say, the pre-1983 units and the number c0 = 299 792 458 m/s that appears in the new, post-1983 units. To illustrate the difference, c is a parameter that appears in the special theory of relativity (SR). In the pre-1983 units agreement between SR and nature is best for a value of c = 299 792 458±1.2 m/s. In the new SI units, it doesn't matter what the number c0 is: SR agrees with nature just as well whatever numerical value is given to c0. Brews ohare (talk) 22:39, 14 September 2009 (UTC)
No I am talking about what I just said, 'If a meter was defined as the distance that real physical light travels in 1/7 second then the speed of real physical light would have to be exactly 7 metres per second'. Are you disputing this statement? Martin Hogbin (talk) 22:41, 14 September 2009 (UTC)

Seems tautological to me. Brews ohare (talk) 22:56, 14 September 2009 (UTC)

No that is not tautology. A tautology would be, the metre is defined as the distance light travels in 1/7 second and the speed of light is defined to be 7 metres per second. Anyway, that is not the point, do you agree that the above statement is correct? Martin Hogbin (talk) 23:00, 14 September 2009 (UTC)

yes. Brews ohare (talk) 23:05, 14 September 2009 (UTC)

So if a meter was defined as the distance that real physical light travels in 1/299,792,458 second then the speed of real physical light would have to be exactly 299,792,458 metres per second, agreed? Martin Hogbin (talk) 23:10, 14 September 2009 (UTC)

Yes again. Brews ohare (talk) 23:53, 14 September 2009 (UTC)

OK. So do you understand the current standard to define the metre as the distance that real physical light travels in 1/299,792,458 second?

## A minor point...

In the last subsection you wrote "an unobtainable reference frequency such as zero or infinite frequency", but the zero frequency limit would be zero, and you couldn't define the metre that way... (The infinite frequency limit would be the c appearing in the Lorentz transformation, so that'd make a helluva sense.) --___A. di M. 19:27, 14 September 2009 (UTC)

I presume that you are referring to the possibility that the photon might have non-zero rest mass. I was just allowing for the possibility that things turned out to be completely different from how we expect and the variation with frequency was the other way round, but they were only example so I am happy to remove the zero suggestion Martin Hogbin (talk) 21:54, 14 September 2009 (UTC)
Yeah. I've heard that according to some flavours of string specul... er... "theory" (*cough*), spacetime is discrete and this would create diffractions effects in vacuum (I know absolutely no further detail about this); but if I have to speculate, I generally like more to make the speculation which requires the least change in existing knowledge. (Also, speed decreasing with frequency would mean group velocity greater than the c of SR, with funny implications with causality, but maybe I'm speculating too much.) --___A. di M. 00:45, 15 September 2009 (UTC)
I had no models in mind when I suggested 'zero' it was just meant to be an example of an unobtainable reference frequency. I have removed it anyway to avoid any possible confusion. Martin Hogbin (talk) 09:46, 15 September 2009 (UTC)

## Comments from Physchim62

### Nature of the speed of light

I'll assume that we are referring to the practical speed of light, which can be neatly defined as

${\displaystyle c_{0}=\lim _{p\to 0}c}$

This can be described as having (at least) five properties:

• it is constant, ie, it doesn't vary over time
• it doesn't vary with frequency
• it is the same as the limiting speed which appears in the Lorentz transformations and SR
• it is the same as the constant linking length and time in GR (sorry if I've not put that well, my GR is pretty lousy)
• it is the same as the constant which appears in various quantum mechanical relations, such as the ratio µ0c0e2/2h (better known as the fine structure constant)

Now we have pretty good experimental evidence for all five of those. Needless to say that they are dictated by theory, but these theories have been tested repeatedly, and have yet to be shown lacking in these respects. SI assumes at least four out of the five (SI is not really very good with GR, by the time you've adding in the necessary extra definition you're effectively using a new set of units!) I'll expand on the consequences (or non-consequences) of that assumption in a moment, but I'll break to let people point out if I'm making a huge error somewhere here… Physchim62 (talk) 10:42, 15 September 2009 (UTC)

### 1972 heterodyne laser measurement of c

In 1972, a team at the NIST laboratories in Boulder, Colorado, measured c0 = 299792458(1.2) m/s, a precision (ur = 4×10−9) about 100-times greater than previous measurements. They did this by comparing the wavelength of the light a stabilized He–Ne laser with the wavelength of the (then-standard) krypton line, and by (fairly directly) comparing the frequency of the light to the frequency of the caesium line that defines the second. c0 = λf.

The uncertainty in this result was entirely due to the characteristics of the krypton light that was, at that time, used to define the metre. The krypton light was not completely monochromatic (no practical light source is), and so didn't (quite) have a single wavelength. In effect, a theoretical limit had been reached as to the accuracy of measurements of the speed of light, at least in that system of units. It is easy to see that there is a theoretical limit in the precision of a metre based on scratches on a metal bar as well – the dimensions and thermal motions of the atoms of the metal: ur = 4×10−9 is at or beyond this theoretical limit (and far beyond the practical limits of metal-bar standards).

The metre could have been redefined in terms of the wavelength of light from a stabilized He–Ne laser, but that really would have been "cooking the books", changing the rules so that this particular experiment always worked! Physchim62 (talk) 10:42, 15 September 2009 (UTC)

### Metrological considerations

There are some fairly subtle metrological reasons why it is "nice" to base the SI on what we believe to be fundamental physical constants. All these constants except one are interrelated by our current Earth-based measurements (a WikiChem Free Beer™ to the editor who finds the "odd-one-out"). You might not think that the speed of light (or the Planck constant for that matter) has much to do with the Avogadro constant, but it does:

${\displaystyle N_{\rm {A}}={\frac {A_{\rm {r}}({\rm {e}})M_{\rm {u}}c_{0}\alpha ^{2}}{2R_{\infty }h}}}$

(see the Avogadro constant article for the gory details, but with the proviso that I wrote that section so any errors are mine)

If you measure the Planck constant, you are also measuring the Avogadro constant, because h is the constant, in all that soup of symbols, that is least-precisely known at present. On the other hand, you could measure the Avogadro constant itself, and use that measurement to find a value for the Planck constant. Both approaches are the subject of active (and extremely expensive) research at the moment: see our article on the kilogram for more details.

These interrelations are based on physical theory, extremely well accepted physical theory at that. But what happens if one of those theories is slightly wrong, as happens fairly regularly in science? What happens is that the different equations no longer add up. Once you have discounted measurement uncertainty, you then have to look for which of the theories is at fault… I've given a simple example from the late 19th century on Talk:Speed of light, where the two conflicting theories were:

1. the speed of light is constant over time
2. the length of bronze bars is constant over time

The constancy of the speed of light won that clash. How we decide which theory is wrong can be as much philosophical and sociological as "scientific", and there is a huge canon of research and opinion (in my PoV, in roughly equal measure) on the question. On the other hand, it is fairly clear, fairly quickly, that something is wrong somewhere.

The speed of light has been fixed in SI units, based on some of the most exhaustively tested theories in physics. Fine. That is useful to find problems elsewhere, so long as our assumptions about the speed of light are correct: problems elsewhere in our theoretical framework are no longer masked by an uncertainty in the value of c0, even if the uncertainty in length measurements is still present. If those theories are wrong, we will end up with equations that don't add up, somewhere or other. When that happens, I'm sure that physics (and all the other sciences that rely on its results) will cope with it, just at it (they) have over the centuries! Physchim62 (talk) 10:42, 15 September 2009 (UTC)

Thanks for your comments. I do not disagree with any of it. Are there any specific points that you think should be included in my statement. Martin Hogbin (talk) 11:10, 15 September 2009 (UTC)
"Everything and nothing" is about the only response to that! The first two sections are points that I would have liked to have seen in your "mainstream description" but didn't find. Then again, it's hardly as if I'm your course tutor, so their absence doesn't matter at all. The third section is an expansion on your current metrology section, but reflects my views and not (necessarily) yours. Physchim62 (talk) 11:29, 15 September 2009 (UTC)
As I said before I have nothing against anything that you said. Maybe I should include some of your first section under the heading 'current theoretical basis'. This page was written as a reply to the claims on the talk page by David Tombe that there is an obvious problem with the exact speed of light when expressed in SI units. I am not attempting to reproduce the complete article here.
The real problem is that we have to have conversations like this here rather than about the real article. Martin Hogbin (talk) 18:17, 15 September 2009 (UTC)
The odd-one-out is the one used to define the candela, isn't it? ___A. di M. 23:16, 28 September 2009 (UTC)
BTW, I guess the reason why h is so imprecisely known is that it's the only one whose numerical value depends on the mass of some piece of metal in Sèvres. If so, you might explain that in the article. ___A. di M. 23:31, 28 September 2009 (UTC)
The candela is based on a defined function intended to model the frequency response of the human eye, so there is no uncertainty in the function. The odd-one-out in metrological terms is the Newtonian gravitation constant, G, which can't be related to any other fundamental constant.
The value of h does depend on the mass of the famous lump of metal, yes, but that's not the limit on its known value at present. It's just hard to measure precisely, that's all. Measuring the Avogadro constant directly is one way to do it, but the most precise measurements come from watt balances. Physchim62 (talk) 08:55, 29 September 2009 (UTC)